Question

simplex method Maximize z = 10x+ 20y Subject to 3x+ 5y ≤ 90 6x + 3y ≤ 72 And x, y ≥ 0

Answer 1

Answer:

    Max. z = 360 at x₁ = 0, x₂ = 18

Step-by-step explanation:

Given,

Maximize z = 10x₁ + 20x₂

subject to: 3x₁ + 5x₂ ≤ 90

                   6x₁ + 3x₂ ≤ 72

           and x₁ ≥ 0, x₂ ≥ 0

We introduce slαck variables x₃ and x₄ and put the problem in a standards form as

Maximize z = 10x₁ + 20x₂ + 0.x₃ + 0.x₄

subject to:

    3x₁ + 5x₂ + x₃ + 0.x₄ = 90

    6x₁ + 2x₂ + 0.x₃ + x₄ = 72

{ add the Simplex tables constructed in the attachment given }

We see that

    zⱼ - cⱼ ≥ 0, for all j

Hence the table gives the optimal solution and they are

    x₁ = 0 and x₂ = 18

∴ zₘₐₓ = 10.0 + 20.18

           = 360 at x₁ = 0, x₂ = 18